# 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.

## Considerations Regarding the Relativist Time and the in Time Traveling

### Author(s): MALVINA BAICA and MIRCEA CÂRDU

**Abstract:** In this paper we examine the problem of time variation in function of the velocity which in the
Theory of Relativity is also considered applicable for the case of the velocities larger then c, the velocity of the
light (high light velocities). For this analyze we apply the ”dual” and ”bipolar” solutions, previously exposed by the
authors [2]. Also, we used the analogy of the respective problem with the similar problem regarding to the (relativist)
dependence of the mass in function of the velocity [1]. Automatically, the problem to ”travel in time” arises, as well
as the methods which could be used for this scope.