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In weighted Orlicz-type spaces S-p,S- (mu) with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the space ...More
In this paper, the authors investigate the initial coefficient bounds for a new generalized subclass of analytic functions related to Sigmoid functions. Also, the relevant connections with the famous classical Fekete?Szegö inequality for these classes are discussed.
In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone ...More