<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (<italic>g</italic>, [, ]) is skew-supersymmetry and satisfies the super Jacobi identity, so it defines the structure of a Lie superalgebra on <italic>g.</italic>In the case of the algebra of differential forms on a supermanifold, we study the graded commutator of graded derivations, graded skew-derivations and a graded derivation, with another graded skew-derivation of the superalgebra of differential forms on a supermanifold.</abstract>

Faculty of Mathematical Sciences Department of Pure Mathematics

On graded derivations of superalgebras

<abstract xmlns="http://www.w3.org/1999/xhtml">In the year 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between “CM” and “IM”. In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of a polynomial function <italic>p</italic>(<italic>f</italic>) of <italic>f</italic> and a homogeneous differential polynomial <italic>P</italic> [<italic>f</italic>] generated by <italic>f</italic>. Our results improve and generalizes the results due to Charak and Lal, S. Lin and W. Lin, and H-Y Xu and Y Hu.</abstract>

Department of Mathematics Raja Rammohunpur

University of North Bengal Raja Rammohunpur

Uniqueness of <italic>p</italic>(<italic>f</italic>) and <italic>P</italic> [<italic>f</italic>] concerning weakly weighted-sharing

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study, the authors establish and generalize some inequalities of Hadamard and Simpson type based on <italic>s</italic>-convexity in the second sense. Some applications are also given and generalized. Examples are given to show the results. The results generalize the integral inequalities in articles of Sarikaya and Xi.</abstract>

Some Hadamard and Simpson type inequalities via <italic>s</italic>-convexity and their applications

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we give some common fixed point theorems for a class of occasionally weakly compatible mappings satisfying contractive conditions of integral type. Our results generalize a host of previously theorems. We also present some illustrative examples which support our main results and show the applicability and validity of these results.</abstract>

Common fixed points under contractive conditions of integral type

<abstract xmlns="http://www.w3.org/1999/xhtml">If <italic>f</italic>, <italic>g</italic>: [<italic>a</italic>, <italic>b</italic>] → 𝕉 are two continuous functions, then there exists a point <italic>c</italic> ∈ (<italic>a</italic>, <italic>b</italic>) such that<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2020-0005_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msubsup><mo>∫</mo><mi>a</mi><mi>c</mi></msubsup><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mrow><mi>d</mi><mi>x</mi><mo>+</mo><mrow><mo>(</mo><mrow><mi>c</mi><mo>-</mo><mi>a</mi></mrow><mo>)</mo></mrow><mi>g</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mrow><msubsup><mo>∫</mo><mi>c</mi><mi>b</mi></msubsup><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mrow><mi>d</mi><mi>x</mi><mo>+</mo><mrow><mo>(</mo><mrow><mi>b</mi><mo>-</mo><mi>c</mi></mrow><mo>)</mo></mrow><mi>f</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>.</mo></mrow></math><tex-math>\int_a^c {f\left(x \right)} dx + \left({c - a} \right)g\left(c \right) = \int_c^b {g\left(x \right)} dx + \left({b - c} \right)f\left(c \right).</tex-math></alternatives></disp-formula>In this paper, we study the approaching of the point <italic>c</italic> towards <italic>a,</italic> when <italic>b</italic> approaches <italic>a.</italic></abstract>

Faculty of Mathematics and Computer Science Department of Computer Science

Faculty of Mathematics and Computer Science Department of Mathematics

Faculty of Science Department of Mathematics and Computer Science

Calculus for the intermediate point associated with a mean value theorem of the integral calculus

<abstract xmlns="http://www.w3.org/1999/xhtml">Assume that <italic>f</italic> and <italic>g</italic> are continuous on <italic>γ, γ</italic> ⊂ 𝔺 is a piecewise smooth path parametrized by <italic>z</italic> (<italic>t</italic>), <italic>t</italic> ∈ [<italic>a</italic>, <italic>b</italic>] from <italic>z</italic> (<italic>a</italic>) = <italic>u</italic> to <italic>z</italic> (<italic>b</italic>) = <italic>w</italic> with <italic>w</italic> ≠ <italic>u</italic> and the <italic>complex Čebyšev functional</italic> is defined by<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2020-0006_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>𝒟</mi><mi>γ</mi></msub><mrow><mo>(</mo><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow><mo>)</mo></mrow><mo>:</mo><mo>=</mo><mfrac><mn>1</mn><mrow><mi>w</mi><mo>-</mo><mi>u</mi></mrow></mfrac><mrow><msub><mo>∫</mo><mi>γ</mi></msub><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></mrow><mi>g</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mi>d</mi><mi>z</mi><mo>-</mo><mfrac><mn>1</mn><mrow><mi>w</mi><mo>-</mo><mi>u</mi></mrow></mfrac><mrow><msub><mo>∫</mo><mi>γ</mi></msub><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></mrow><mi>d</mi><mi>z</mi><mfrac><mn>1</mn><mrow><mi>w</mi><mo>-</mo><mi>u</mi></mrow></mfrac><mrow><msub><mo>∫</mo><mi>γ</mi></msub><mrow><mi>g</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></mrow><mi>d</mi><mi>z</mi><mo>.</mo></mrow></math><tex-math>{{\cal D}_\gamma}\left({f,g} \right): = {1 \over {w - u}}\int_\gamma {f\left(z \right)} g\left(z \right)dz - {1 \over {w - u}}\int_\gamma {f\left(z \right)} dz{1 \over {w - u}}\int_\gamma {g\left(z \right)} dz.</tex-math></alternatives></disp-formula>In this paper we establish some Grüss type inequalities for <italic>𝒟</italic> (<italic>f</italic>, <italic>g</italic>) under some complex boundedness conditions for the functions <italic>f</italic> and <italic>g</italic>.</abstract>

A refinement of Grüss inequality for the complex integral

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we study a class of univalent functions <italic>f</italic> as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2020-0007_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mo>Re</mo><mrow><mo>{</mo><mrow><mfrac><mrow><mi>z</mi><mrow><mo>(</mo><mrow><msubsup><mstyle><mi>J</mi></mstyle><mn>1</mn><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi></mrow></msubsup><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mo>'</mo></mrow><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mi>γ</mi></mrow><mo>)</mo></mrow><msubsup><mstyle><mi>J</mi></mstyle><mn>1</mn><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi></mrow></msubsup><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>+</mo><mi>γ</mi><msup><mi>z</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><msubsup><mstyle><mi>J</mi></mstyle><mn>1</mn><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi></mrow></msubsup><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mo>'</mo><mo>'</mo></mrow></mfrac></mrow><mo>}</mo></mrow><mo>></mo><mi>β</mi><mo>.</mo></mrow></math><tex-math>{\mathop{\rm Re}\nolimits} \left\{{{{z\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)'} \over {\left({1 - \gamma} \right){\bf{J}}_1^{\lambda,\mu}f\left(z \right) + \gamma {z^2}\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)''}}} \right\} > \beta.</tex-math></alternatives></disp-formula>A necessary and sufficient condition for a function to be in the class <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2020-0007_eq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>A</mi><mi>γ</mi><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>ν</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mi>n</mi><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></mrow></math><tex-math>A_\gamma ^{\lambda,\mu,\nu}\left({n,\beta} \right)</tex-math></alternatives></inline-formula> is obtained. Also, our paper includes linear combination, integral operators and we introduce the subclass <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2020-0007_eq_003.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>A</mi><mrow><mi>γ</mi><mo>,</mo><msub><mi>c</mi><mi>m</mi></msub></mrow><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>ν</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></mrow></math><tex-math>A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right)</tex-math></alternatives></inline-formula> consisting of functions with negative and fixed finitely many coefficients. We study some interesting properties of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2020-0007_eq_004.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>A</mi><mrow><mi>γ</mi><mo>,</mo><msub><mi>c</mi><mi>m</mi></msub></mrow><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>ν</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></mrow></math><tex-math>A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right)</tex-math></alternatives></inline-formula>.</abstract>

College of Science, Department of Mathematics

Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients II

<abstract xmlns="http://www.w3.org/1999/xhtml">Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.</abstract>

Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, we find certain results on Ruscheweyh operator using differential inequality. In particular, we find sufficient conditions for starlike and convex functions.</abstract>

A differential inequality involving Ruscheweyh operator and univalent functions

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients |<italic>a</italic>2| and |<italic>a</italic>3| for the functions in these classes. Also we investigate upper bounds for the Fekete-Szegö functional and second Hankel determinant for these classes.</abstract>

Certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers

AHEAD OF PRINT

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General Mathematics

 Publishing House and Owner: Lucian Blaga University of Sibiu, Romania   General Mathematics publishes high quality papers on pure and applied mathematics. To be published in this journal, a paper must contain new ideas and be of interest to a wide range of readers. Survey papers are also welcome.The journal appears in 2 numbers per year and has been published since 1993.It is edited by the Department of Mathematics and Informatics of the “Lucian Blaga” University of Sibiu.  The purpose of General Mathematics is to provide an outlet for high quality original research in all areas of analysis or that having applications in economics, engineering, the life sciences, physics and statistical decision theory.  Coverage touches on a wide variety of topics, including:   Functional analysis and operator theory  Real and harmonic analysis　  Complex analysis　  Numerical analysis　  Applied mathematics　  Partial differential equations　  Dynamical systems　  Control and Optimization　  Probability　  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 