<abstract xmlns="http://www.w3.org/1999/xhtml">We study submanifolds of a quaternionic projective space, it is of great interest how to pull down some formulae deduced for submanifolds of a sphere to those for submanifolds of a quaternionic projective space.</abstract>

Department of Mathematics, Azarbaijan shahid Madani University, Iran

On submersion and immersion submanifolds of a quaternionic projective space

<abstract xmlns="http://www.w3.org/1999/xhtml">In this note we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials. We also discuss several different expressions for the nth derivative of exp(1/<italic>x</italic>). A new representation of this derivative is given in terms of exponential polynomials.</abstract>

Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/<italic>x</italic>)

<abstract xmlns="http://www.w3.org/1999/xhtml">Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on <italic>MS</italic>(<italic>QE</italic>)4 for both the Riemannian and Lorentzian cases.</abstract>

Department of Mathematics, Jadavpur University, India

Department of Mathematics, Institute of Science, Banaras Hindu University, India

Department of Mathematics, Jadavpur University, India.

On some classes of mixed-super quasi-Einstein manifolds

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we study the geometry of the pseudo-slant submanifolds of a cosymplectic space form. Necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, pseudo-slant product, mixed geodesic and totally geodesic in cosymplectic manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifold in a cosymplectic manifold and cosymplectic space form.</abstract>

Department of Statistic, Faculty of Arts and Sciences, Amasya University, Turkey

Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpasa University, Turkey

Pseudo-slant submanifolds in cosymplectic space forms

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we establish some vector inequalities for two operators related to Schwarz and Buzano results. We show amongst others that in a Hilbert space <italic>H</italic> we have the inequality
<disp-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/ausm-2016-0005_i1.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>[</mo><mrow><msup><mrow><mrow><mo>〈</mo><mrow><mfrac><mrow><msup><mrow><mrow><mo>|</mo><mtext>A</mtext><mo>|</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>|</mo><mtext>B</mtext><mo>|</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mtext>x</mtext><mo>,</mo><mtext>x</mtext></mrow><mo>〉</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mrow><mo>〈</mo><mrow><mfrac><mrow><msup><mrow><mrow><mo>|</mo><mtext>A</mtext><mo>|</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>|</mo><mtext>B</mtext><mo>|</mo></mrow></mrow><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mtext>y</mtext><mo>,</mo><mtext>y</mtext></mrow><mo>〉</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>+</mo><mrow><mo>|</mo><mrow><mrow><mo>〈</mo><mrow><mfrac><mrow><msup><mrow><mrow><mo>|</mo><mtext>A</mtext><mo>|</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>|</mo><mtext>B</mtext><mo>|</mo></mrow></mrow><mn>2</mn></msup></mrow><mtext>2</mtext></mfrac><mtext>x</mtext><mo>,</mo><mtext>y</mtext></mrow></mrow><mo>〉</mo></mrow></mrow><mo>|</mo></mrow><mo>]</mo></mrow><mo>≥</mo><mrow><mo>|</mo><mrow><mrow><mo>〈</mo><mrow><mi>Re</mi><mo> </mo><mo stretchy="false">(</mo><mtext>B</mtext><mo>*</mo><mtext>A</mtext><mo stretchy="false">)</mo><mo> </mo><mtext>x</mtext><mo>,</mo><mtext>y</mtext></mrow><mo>〉</mo></mrow></mrow><mo>|</mo></mrow></mrow></math><tex-math>$${1 \over 2}\left[ {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{x}},{\rm{x}}} \right\rangle ^{1/2} \left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{y}},{\rm{y}}} \right\rangle ^{1/2} + \left| {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over {\rm{2}}}} {\rm{x}},{\rm{y}}\right\rangle } \right|} \right] \ge \left| {\left\langle {{\mathop{\rm Re}\nolimits} ({\rm{B}}*{\rm{A}})\,{\rm{x}},{\rm{y}}} \right\rangle } \right|$$</tex-math></alternatives></disp-formula>
for <italic>A</italic>, <italic>B</italic> two bounded linear operators on <italic>H</italic> such that R<italic>e</italic> (<italic>B</italic>*<italic>A</italic>) is a nonnegative operator and any vectors <italic>x</italic>, <italic>y</italic> ∈ <italic>H</italic>.Applications for norm and numerical radius inequalities are given as well.</abstract>

Some vector inequalities for two operators in Hilbert spaces with applications

<abstract xmlns="http://www.w3.org/1999/xhtml">In the paper, the authors find necessary and sufficient conditions such that a function related to the Catalan-Qi function, which is an alternative generalization of the Catalan numbers, is logarithmically complete monotonic.</abstract>

Institute of Mathematics, Henan Polytechnic University, China; College of Mathematics, Inner Mongolia University for Nationalities, China; Department of Mathematics, College of Science, Tianjin Polytechnic University, China

School of Mathematics and Informatics, Henan Polytechnic University, China

Logarithmically complete monotonicity of a function related to the Catalan-Qi function

<abstract xmlns="http://www.w3.org/1999/xhtml">Using Euler-type identities some new generalizations of Steffensen’s inequality for <italic>n</italic>–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.</abstract>

Faculty of Textile Technology, University of Zagreb, Croatia

Faculty of Civil Engineering, University of Rijeka, Croatia

Generalizations of Steffensen’s inequality via some Euler-type identities

<abstract xmlns="http://www.w3.org/1999/xhtml">The maximum of the conditional hazard function is a parameter of great importance in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates of the first derivative of the conditional hazard function, we establish uniform convergence properties and asymptotic normality of an estimate of the maximum in the context of independence data.</abstract>

Laboratory of Mathematics, Sidi Bel Abbes University

Stochastic Models Statistics and Applications Laboratory, Moulay Tahar University of Saida

Consistency rates and asymptotic normality of the high risk conditional for functional data

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, with use of Lyapunov functional, we investigate asymptotic stability of solutions of some nonlinear differential equations of third order with delay. Our results include and improve some well-known results in the literature.</abstract>

Department of Mathematics, University of Oran 1, Ahmed Benbella, Algeria

Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we focus on the time-varying shortest path problem, where the transit costs are fuzzy numbers. Moreover, we consider this problem in which the transit time can be shortened at a fuzzy speedup cost. Speedup may also be a better decision to find the shortest path from a source vertex to a specified vertex.</abstract>

Department of Mathematics, Faculty of Basic Sciences, University of Qom, Iran

The time-varying shortest path problem with fuzzy transit costs and speedup

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.</abstract>

Department of Mathematics, Govt. Nagarjuna P. G. College of Science, India

Some common random fixed point theorems for contractive type conditions in cone random metric spaces

AHEAD OF PRINT

Volume 15 (2023): Issue 2 (December 2023)

Volume 15 (2023): Issue 1 (November 2023)

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Acta Universitatis Sapientiae, Mathematica

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