Sahand Communications in Mathematical Analysis
Volume:19 Issue: 1, Winter 2022

In this paper, focus is on the study of spectrum and the spectral properties of bounded linear operators in intuitionistic fuzzy pseudo normed linear spaces(IFPNLS). It is done by studying regular value, resolvent set, spectrum of a linear operator in IFPNLS. Also, some properties of spectrum and resolvent of strongly intuitionistic fuzzy bounded(IFB) linear operators in IFPNLS are being developed. It is observed that, for a linear operator $P$ in an IFPNLS, the resolvent set $rho(P)$ and spectrum $sigma(P)$ are nonempty, $rho(P)$ is open and $sigma(P)$ is closed set.

In this paper, we introduce a three-step implicit iteration scheme with errors for finite families of nonexpansive and uniformly $L$-Lipschitzian asymptotically generalized $Phi$-hemicontractive mappings in real Banach spaces. Our new implicit iterative scheme properly includes several well known iterative schemes in the literature as its special cases. The results presented in this paper extend, generalize and improve well known results in the existing literature.

Weighted integral inequalities for general integral operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for negative $p$ and $q$. We give some new lemmas which will be frequently used in the proofs of the main theorems.

Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationshipbetween fuzzy continuity of linear operators and fuzzy boundedness is investigated. The uniform boundedness theorem is then discussed, so too is the norm of a linear operator. Finally, the open mapping theorem is proved for each of the three defined fuzzy topologies, and the closed graph theorem is studied.

The concept of summability plays a central role in finding formal solutions of partial differential equations. In this paper, we introduce the concept of Cesàro summability in an intuitionistic fuzzy $n$-normed linear space (IFnNLS). We show that Cesàro summability method is regular in an IFnNLS, but  Cesàro summability does not imply usual convergence in general. Further, we search for additional conditions under which the converse holds.

Let $mathcal M$ be a  class of (mono)morphisms in a category $mathcal A$. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (${mathcal A}$,${mathcal M}$).In this paper, we take $mathcal A$ to be the category {bf Pos}-$S$ of $S$-posets over a posemigroup $S$, and ${mathcal M}_{dc}$ to be the class of down closed embeddings and study the categorical properties, such as limits and colimits, of the  pair (${mathcal A}$,${mathcal M}$). Injectivity with respect to this class of monomorphisms have been studied by Shahbaz et al., who used it to obtain  information about regular injectivity.

This article introduces the notion of L$_p$-C$^*$-semi-inner product space, a generalization of the concept of C$^*$-semi-inner product space  introduced by Gamchi et al., where we consider H"{o}lder's inequality instead of Cauchy Schwartz' inequality. We establish some basic results L$_p$-C$^*$-semi-inner product spaces, analogous to those valid for C$^*$-semi-inner product spaces and Hilbert C$^*$-modules.

We extend the definitions of $nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $int P(y)f(y) dy$ and $int int P(y,z) f(y,z) dy   dz$ are deduced. Using obtained identities, positivity of these expressions are characterized for  higher order $nabla-$convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.