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

Indexed in:
Mathematical Reviews
Zentralblatt MATH
EBSCO

Front cover

# Volume 13 (2021), Number 1-2

## Three Variables Fractional Analogues of Trapezium Like Inequalities

### Author(s): MUHAMMAD UZAIR AWAN, MARCELA V. MIHAI, MUHAMMAD ZAKRIA JAVED, MUHAMMAD ASLAM NOOR and KHALIDA INAYAT NOOR

Abstract: The aim of this paper is to derive some new fractional analogues of trapezium like inequalities essentially using a new three variable extension of Riemann-Liouville fractional integrals. In order to establish the main results of the paper we use the three variable convexity property of the functions.

## Grüss Type Inequalities for Various Kinds of Fractional Integration

### Author(s): GABRIELA CRISTESCU and SORIN-HORAȚIU HOARĂ

Abstract: Some new and useful Grüss type inequalities using Riemann-Liouville fractional integral, Erdélyi-Kober integral operator and Katugampola fractional integral are established. The inequalities are sharp.

## Ulam-Hyers Stability of Some Integral Equations

### Author(s): MARIA DOBRIȚOIU

Abstract: This paper contains some results regarding the property of the Ulam-Hyers stability of a Fedholm type, a Volterra type and a Fredholm-Volterra type respectively, integral equation. The results presented in this paper were obtained using the Picard operator technique and complete the study of the solution of these integral equations.

## Improvements of Jensen-Mercer Type Discrete Inequalities for Convex Functions on Finite Intervals

### Author(s): SILVESTRU SEVER DRAGOMIR

Abstract: In this paper we obtain some new refinements of Mercer’s discrete inequality for univariate functions defined on finite intervals and provide some examples for particular functions of interest.

## Strongly General Bivariational Inequalities

### Author(s): MUHAMMAD ASLAM NOOR and KHALIDA INAYAT NOOR

Abstract: In this work, we introduce and study some new classes of biconvex functions involving an arbitrary bifunction, which are called strongly biconvex functions. Some new relationships among various concepts of strongly biconvex functions have been established. We have shown that the optimality conditions for the biconvex functions can be characterized by a class of bivariational inequalities. An auxiliary principle technique is used to propose proximal point methods for solving bivariational inequalities. We also discussed the conversance criteria for the suggested methods under pseudo-monotonicity. Several special cases are discussed as applications of our main concepts and results.

## Analysis of Consumer Prices in Romania by Multiple Regression

### Author(s): ANAMARIA POPESCU

Abstract: This article describes a correlation between the annual index of total consumer prices, the annual index of consumer prices of food, the annual index of consumer prices of non-food products and the annual index of consumer prices of services, using a multiple regression model. The use of statistical-econometric models in macroeconomic analyzes can be used successfully by using the simple linear regression model, but multiple linear regression is preferred, because several factors influence the evolution of the resulting variables. In the case of multiple linear regression, the factors we have in mind must be identified and they must be included in the reconnected model following the same graph representation procedure, establishing the correlation chart to inventory the point cloud and the evolution of each variable, following as their basis to perform data interpretation and moreover by establishing the value of regression parameters to identify quantified intensity, direction of influenceor, in other words, the intensity of the correlation between the factors considered. In order for the inference based on the valid results of the linear regression to be valid, a set of hypotheses was tested, known as the normal classical model of multiple regression.

## Analytical Analysis and Graphical Presentations of Three Dimensional Influence Functions Within a Thermoelastic Half-Layer

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

Abstract: This paper is devoted to analytical analysis of the solution for a boundary value problem given partially in the works: [18] V. Șeremet, A three-dimensional generalized BVP of thermoelasticity for a layer: Green’s functions and integration formula, TJMM, vol. 10, no. 2, p. 121-129, 2018 and [19] V. Șeremet and I. Crețu, Three-dimensional influence functions and integration formula for many boundary value problems within a thermoelastic half-layer, TJMM, vol. 12, no, 1, p. 45-58, 2020. The mentioned above solutions satisfy equations of thermoeasticity and boundary conditions only, but derived Green’s functions for thermoelastic displacements, caused by a unit point heat source do not vanish at infinity. Thus, the application simultaneous of analytical and graphical methods permed us to obtain exact analytical solutions which vanish at the infinity. In fact, to derive exacts analytical expressions for main termoelastic displacements Green’s functions (MTDGFs) was necessary to be omitted in the solutions given in [18] and [19] the terms which do not vanish at infinity without affecting the other main equations. Graphical presentation of derived exact analytical expressions for a three-dimensional MTDGFs, plotted by using soft Maple 18 is included.

## Fixed Point Results for Some Contraction Type Mappings in $A$-Metric Spaces

### Author(s): ISA YILDIRIM

Abstract: In the present paper, we define an analogue of Hardy-Rogers type contraction in $A$-metric spaces and prove a fixed point theorem for such mappings under appropriate conditions in such spaces. Also, we give some results for Kannan, Chatterjea, Reich, Ciric type contraction mappings in $A$-metric spaces. Our results generalize many known results in the fixed point theory.

## On the Stability and Convergence of Mann Iteration Process in Convex $A$-Metric Spaces

### Author(s): ISA YILDIRIM

Abstract: In this paper, firstly, we introduce the concept of convexity in $A$-metric spaces and show that Mann iteration process converges to the unique fixed point of Zamfirescu type contractions in this newly defined convex $A$-metric space. We give also an example concerning with this convergence. Secondly, we define the concept of stability in convex $A$-metric spaces and establish stability result for the Mann iteration process considered in such spaces. Our results carry some well-known results from the literature to convex $A$-metric spaces.

## Boundary Value Problems for Hadamard-Caputo Implicit Fractional Differential Inclusions in a Banach Space

### Author(s): AHMED ZAHED, SAMIRA HAMANI and JOHN R. GRAEF

Abstract: The authors prove the existence of solutions to a boundary value problem for an implicit fractional differential inclusion of Hadamard-Caputo type in a Banach space. The technique of proof makes use of a set-valued analog of Mönch’s fixed point theorem combined with a measure of noncompactness. They present an example to illustrate the main results.