Sahand Communications in Mathematical Analysis
Volume:19 Issue: 4, Autumn 2022

In this work, we introduce an iterative algorithm for solving the split feasibility problem on zeros of the sum of monotone operators and fixed point sets and also solving the fixed point problem of a nonexpansive mapping. This algorithm is a modification of the method based on the inertial and Mann viscosity-type methods. By assuming the existence of solutions, we show the strong convergence theorems of the constructed sequences. Finally, we also apply the proposed algorithm to related problems in Hilbert spaces.

In this article we have introduced the sequence space $m(\phi,d)$ and $m(M,\phi,d)$ of W. L. C. Sargent type in a metric space $(X, d)$ on generalising the sequence space $m(\phi)$ and we have defined these sequence spaces using the Orlicz function $M$. We have investigated their different properties like solidness, symmetricity, monotone, sequence algebra, completeness etc. We have established some inclusion results involving the space $m(M,\phi,d)$ and some of the existing sequence spaces. We have provided suitable examples and discussed in detail, in order to justify the failure cases and the definitions we have introduced. The results established in this article generalized and unifies several existing results.

In this paper, we investigate  Godunova type inequality for Sugeno integrals in two cases. At the first case, we suppose that the inner integral is the  Riemann integral and the remaining two integrals are of Sugeno type. At the second case, all the integrals are assumed Sugeno integrals. We present several examples to illustrate  validity of our results.

In this paper, we study the concept of multipliers for the continuous $g$-Bessel families in Hilbert spaces. We present necessary conditions for invertibility of multipliers for the continuous $g$-Bessel families and sufficient conditions for invertibility of multipliers for continuous $g$-frames.

The aim of this article is to obtain some necessary and sufficient conditions for  functions, whose coefficients are probabilities of the Miller-Ross-type Poisson distribution series, to belong to certain subclasses of analytic and univalent functions. Furthermore, we consider an integral operator related to the Miller-Ross type Poisson distribution series.

In this paper, we introduce the notion of deferred statistical convergence in the neutrosophic normed spaces as an extension of statistical convergence, $\lambda$-statistical convergence, and lacunary statistical convergence. We investigate a few fundamental properties of the newly introduced notion. Finally, we introduce the concept of deferred statistical Cauchy sequence and show that deferred statistical Cauchy sequences are equivalent to deferred statistical convergent sequences in the neutrosophic normed spaces.

We generalize a theorem due to Jarosz, by proving that every almost $n$-multiplicative linear functional on Banach algebra $A$ is automatically continuous. The relation between almost multiplicative and almost $n$-multiplicative linear functional on Banach algebra $A$ is also investigated. Additionally, for commutative Banach algebra $A$, we prove that every almost Jordan homomorphism $\varphi:A\longrightarrow \mathbb{C}$ is an almost $n$-Jordan homomorphism.

In this paper, some conditions have been improved so that the function $g(z)$ is defined as $g(z)=1+\sum_{k\ge 2}^{\infty}a_{n+k}z^{n+k}$, which is analytic in unit disk $U$, can be in more specific subclasses of the $S$ class, which is the most fundamental type of univalent function. It is analyzed some characteristics of starlike and convex functions of order $2^{-r}$.

In this article, we will study the existence and uniqueness of optimal common fixed points for self-mappings in metric spaces with w-distance. We obtain generalizations of the Kocev and Rako\v{c}evi\'{c} fixed point theorems. The obtained results do not require the continuity or the condition $(C;k)$ of maps,  but require the weaker condition $(W)$. We also improve some of our results when the metric space is equipped with a w$_0$-distance. In this way, we get new existence results for non-cyclic quasi-contraction mappings of the Fisher type.

In this paper we define a new subclass $S_{LH}(k, \gamma; \varphi)$ of log-harmonic mappings, and then basic properties such as dilations, convexity on one direction and convexity of log functions of convex- exponent product of elements of that class are discussed. Also we find sufficient conditions on $\beta$ such that $f\in S_{LH}(k, \gamma; \varphi)$ leads to $F(z)=f(z)|f(z)|^{2\beta}\in S_{LH}(k, \gamma, \varphi)$. Our results generalize the analogues of the earlier works in the combinations of harmonic functions.