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

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.

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.

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.

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.

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.

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.

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.

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.

In this paper the problem of hypothesis testing is considered as an estimation problem within a decision-theoretic framework for estimating the accuracy of the test. The usual p-value is an admissible estimator for the one-sided testing of the scale parameter under the squared error loss function in the Pareto distribution. In the presence of nuisance parameter for model, the generalized p-value is inadmissible. Even though the usual p-value and the generalized p-value are inadmissible estimators for the one-sided testing of the shape parameter, it is difficult to exhibit a better estimator than the usual p-value. For the two-sided testing, although the usual p-value is generally inadmissible, it is remained as an estimator for the two-sided testing of the shape parameter.

This paper deals with new results on Gruss inequality by using recent fractional integral operators. In fact, based on the (k, s, h) −Riemann-Liouville and the (k, h) −Hadamard fractional operators, we establish several integral results. For our results, some very recent results on the paper: [A Gr¨uss type inequality for two weighted functions. J. Math. Computer Sci., 2018.] can be deduced as some special cases.