‎In this paper‎, ‎for a singular perturbation problem consist of the Cauchy-Euler equation with local and non-local boundary conditions‎. ‎We investigate the condition of the self-adjoint and the non-self-adjoint‎, ‎also look for the formation or non-formation of boundary layers for local boundary conditions using the Frequent uniform limit method‎. ‎Also‎, ‎for the state of non-local conditions‎, ‎we convert the non-local boundary conditions into local conditions by finding the fundamental solution and then obtaining the necessary conditions with the help of the 4-step method‎. ‎Finally‎, ‎we determine the formation or non-formation of a boundary layer for non-local conditions such as local conditions‎.

The purpose of this article is to generalize Cebysev type inequalities for double integrals involving a weight function.By using an integral transform that is a weighted Montgomery identity, we obtained a generalized form of weighted Cebysev type inequalities in $L_m,, mgeq 1$ norm of differentiable functions. Also, we give some applications of the probability density function.

In this paper, we introduce new concepts of fuzzy $(\\gamma,\\beta )$-contraction and prove some fixed point results for fuzzy $(\\gamma,\\beta )$-contractions in complete non-Archimedean fuzzy metric spaces. Later, we define a fuzzy $(\\gamma,\\beta )$-weak contraction and establish some new fixed point results for fuzzy $(\\gamma,\\beta )$-weak contractions. Also, some examples are supplied in order to support the useability of ourresults.

The aim of this paper is to define and study the concept of $\mathcal{I}$-convergence in fuzzy cone normed space which is a generalization of R. Saadati and S. M. Vaezpour type fuzzy normal space. We also obtained some basic properties of $\mathcal{I}$-convergence. In fuzzy cone normed space, $\mathcal{I}$-limit point and $\mathcal{I}$-cluster point were defined and studied.

In this paper, we obtain a new modified iteration process in the setting of CAT(0) spaces involving generalized $alpha$-nonexpansive mapping. We prove strong and $Delta$ convergence results for approximating fixed point via newly defined iteration process. Further, we reconfirm our results by non trivial example and tables.

In this work, we study two uncoupled quasistatic problems for thermo viscoplastic materials. In the model of the equation of generalised thermo viscoplasticity, both the elastic and the plastic rate of deformation depend on a parameter $\theta $ which may be interpreted as the absolute temperature. The boundary conditions considered here as displacement-traction conditions as well as unilateral contact conditions. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem, reducing the isotherm problem to an ordinary differential equation in a Hilbert space.

In this paper, we introduce the notion of woven g-fusion frames in Hilbert spaces. Then, we present sufficient conditions for woven g-fusion frames in terms of woven frames in Hilbert spaces. We extend some of the recent results of standard woven frames and woven fusion frames to woven g-fusion frames. Also, we study perturbations of woven g-fusion frames.

In this paper, we discuss the existence results for a class of hybrid initial value problems of Riemann-Liouville fractional differential equations. Our investigation is based on the Dhage hybrid fixed point theorem, remarks and some special cases will be discussed. The continuous dependence of the unique solution on one of its functions will be proved.

We define a new subclass of univalent harmonic mappings using multiplier transformation and investigate various properties like necessary and sufficient conditions, extreme points, starlikeness, radius of convexity. We prove that the class is closed under harmonic convolutions and convex combinations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

In this paper, the notion of $p$-hybrid $L$-fuzzy contractions in the framework of $b$-metric space is introduced. Sufficient conditions for existence of common $L$-fuzzy fixed points under such contractions are also investigated. The established ideas are generalizations of many concepts in fuzzy mathematics. In the case where our postulates are reduced to their classical variants, the concept presented herein merges and extends several significant and well-known fixed point theorems in the setting of both single-valued and multi-valued mappings in the corresponding literature of discrete and computational mathematics. A few of these special cases are pointed out and discussed. In support of our main hypotheses, a nontrivial example is provided.