# Journal of Mathematical Extension Volume:16 Issue: 5, May 2022

• تاریخ انتشار: 1400/07/14
• تعداد عناوین: 10
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• G. Farid, V.N. Mishra* Page 1

The aim of this study is to establish some new Caputo fractional integral inequalities. By applying definition of (h − m)-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Furthermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from (h − m)-convexity, see Remark 1.3.

Keywords: Convex function, (h − m)-convex function, Caputo fractional derivatives
• F. Movahedi*, M. H. Akhbari Page 2

Let G be a graph with n vertices and m edges. The minimum edge dominating energy is defined as the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of the graph G. In this paper, some lower and upper bounds for the minimum edge dominating energy of graph G are established.

Keywords: Minimum edge dominating energy, Eigenvalue, Adjacency matrix, Line graph
• S. Kumar Datta, S. Sarkar*, G. Chakraborty, A. Manna Page 3

Let f be a transcendental entire function defined in the open complex plane C. A difference-monomial generated by f is an expression of the form F = f n (f m − 1) Yd j=1 (f(z + cj ))νj , where n, m and νj are all non-negative integers. Now for the sake of definiteness let us take, Mi[f] = f n (f m − 1) Yi j=1 (f(z + cj ))νj , where 1 ≤ i ≤ d. If M1[f], M2[f], . . . , Mn[f] are such monomials in f as defined above, then ψ[f] = a1M1[f] + a2M2[f] + . . . + anMn[f] where ai 6= 0 (i = 1, 2, . . . , n) is called a difference-polynomial generated by f. In this paper, we compare the Valiron defect with the relative Nevanlinna defect of a particular type of differential-difference polynomial generated by a transcendental entire function with respect to integrated moduli of logarithmic derivative. Some examples are provided in order to justify the results obtained.

Keywords: Entire function, meromorphic function, relative Nevanlinna defect, relative Valiron defect, difference polynomial, integrated moduli of logarithmic derivative
• S. S. Mansouri, M. Gachpazan, N. Ahmady *, E. Ahmady Page 4

This paper seeks to investigate the existence and uniqueness of solutions to fuzzy differential equations driven by Liu’s process. For this purpose , we prove a novel existence and uniqueness theorem for fuzzy differential equations under Local Lipschitz and monotone conditions. This result allows us to consider and analyze solutions to a wide range of nonlinear fuzzy differential equations driven by Liu’s process. To illustrate the main advantage of the approach some examples are finally given.

Keywords: Fuzzy number, Fuzzy differential equation, Liu’s process, Credibility space
• A. Peyravi* Page 5

This work is concerned with the initial boundary value problem for a nonlinear viscoelastic Petrovsky wave equation utt + ∆2 u − Z t 0 g(t − τ )∆2 u(τ )dτ − ∆ut − ∆utt + ut|ut| m−1 = u|u| p−1 . Under suitable conditions on the relaxation function g, the global existence of solutions is obtained without any relation between m and p. The uniform decay of solutions is proved by adapting the perturbed energy method. For p > m and sufficient conditions on g, an unboundedness result of solutions is also obtained.

Keywords: Global existence, general decay, exponentialgrowth, Petrovsky equation

A bounded linear operator T on Banach space X is subspace convex-cyclic for a subspace M if there exists a vector x ∈ X such that Co(orb(T, x)) ∩ M is dense in M. We construct examples of subspace convex-cyclic operator that is not convex-cyclic. In particular, we prove that every convex-cyclic operator on the separable Banach space X is a subspace convex-cyclic operator for some pure subspace M of X.

Keywords: Hypercyclicity, Convex hull, Subspace convexcyclic operators
• S. Barootkoob*, H. Lakzian, Z. D. Mitrovi´c Page 7

In this paper, we introduce a weak MT -cyclic Reich type contractions and obtain the existence theorems for best proximity point for self-mappings defined on the complete metric spaces. Our results improve and generalize some results in literature. Also, we give some applications of our results to solving some classes of non-linear integral and differential equations.

Keywords: Cyclic map, best proximity point, weakMT -cyclic Reich type contraction
• H. Faraji*, S. Radenović Page 8

In this paper, we introduce the concept of F−G−contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F−metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results.

Keywords: Fixed point, F−Metric spaces, F−G−contraction