ISSN: 2067-239X
ISSN(on-line): 2067-239X

Indexed in:
Mathematical Reviews
Zentralblatt MATH

Front cover

# Volume 12 (2020), Number 1

## Some New Simpson-Like Type Inequalities Via Preqausiinvexity

### Author(s): T. CHIHEB, N. BOUMAZZA and B. MEFTAH

Abstract: In this paper, we first establish a new integral identity which represent a partielle result, by using this identity we derive some new Simpson like type integral inequalities for functions whose second derivatives are prequasiinvex functions. we also discuss some special cases where the second derivatives are monotonous functions. At the end we give some applications to special means.

## An Application of the Admissibility Types in $b$-Metric Spaces

### Author(s): MARIA DOBRIȚOIU

Abstract: In this paper we present a fixed point theorem for the solution of the nonlinear Fredholm integral equation $x(t)= ∫ab K(t,r,x( r),x(g( r)))dr +f(t) , t∈[ a ,b ],$ as an application of a result of S. Radenović et al., in [14]. In order to obtain this existence result, we used also, the notions of admissibility types defined on a $b$-metric space, in [17].

## Modified $S$-Metric Spaces and Some Fixed Point Results

### Author(s): ABDULLAH KARAMI, SHABAN SEDGHI, NABI SHOBE and ZORAN D. MITROVIĆ

Abstract: In this paper, a structure of modified $S$-metric spaces is introduced which can be viewed a generalization of both $S$-metric and $Sb$-metric spaces. Also, the notions of $S˜$ -contractive mappings in the modified $S$-metric spaces is given. We also investigate the existence of fixed point for such mappings under various contractive conditions. We provide example and an application to illustrate the results presented herein.

## Chebyshev Type Inequalities Involving Generalized Proportional Fractional Integral Operators

### Author(s): İLKER MUMCU, ERHAN SET and ARTION KASHURI

Abstract: A number of definition of fractional integral operators have, recently, been presented. In [11], Jarad et al. introduced the proportional generalized fractional integrals. In this paper, we motivated essentially by the earlier works and established some Chebyshev type inequalities for synchronous functions involving generalized proportional fractional integral operators. Also we have results containing confluent hypergeometric functions and incomplete gamma functions.

## A Problem With Second Kind’s Nonlocal Condition for Pseudohyperbolic Equation

### Author(s): AICHA SAKHRI and AHCENE MERAD

Abstract: In this article, the Faeod-Galerkin method is proposed for solving a pseudohyperbolic type equation with an integral condition. We construct a discrete numerical solution of the approximate problem.

## Three-Dimensional Influence Functions and Integration Formulas for Many Boundary Value Problems Within a Thermoelastic Half-Layer

### Author(s): VICTOR ȘEREMET and ION CREȚU

Abstract: The aim of this paper is the constructing of the main thermoelastic displacements Green’s functions (MTDGFs) for a generalized 3D BVP of uncoupled thermoelasticity for a half-layer. To reach this aim are derived structural formulas for MTDGFs expressed via respective Green’s functions for Poisson’s equation (GFPE) by using harmonic integral representations method (HIRM). These structural formulas are validated by the checking the equations of thermoelasticity with respect to point of application the heat source and the nonhomogeneous Poisson’s equation with respect to point of response in which the thermoelastic displacements appeared. In addition, they satisfy boundary conditions for temperature Green’s function with respect to point application the displacements and to mechanical boundary conditions with respect to point of application the heat source. The thermoelastic volume dilatation (TVD) derived separately from respective integral representations have to be equal to the TVD derived by using structural formulas for MTDGFs. The final analytical expressions for MTDGFs obtained on the base of mentioned above structural formulas for eight new 3D BVPs of thermoelasticity within half-layer contain Bessel functions of the zero-order and of the second type. Finally, the integration formulas for thermal displacements and stresses, created by inner heat source and by the thermal data given of the surface of the half-layer are presented also.