Deutsch paths and their enumeration
ODAM-Vol. 4 (2021), Issue 1, pp. 12 – 18 Open Access Full-Text PDF
Helmut Prodinger
Abstract: A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection.
Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator
OMA-Vol. 5 (2021), Issue 1, pp. 42 – 50 Open Access Full-Text PDF
Timilehin Gideon Shaba
Abstract: In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.
Fixed point theorems for generalized \(\left( \psi ,\varphi ,F\right)\)-contraction type mappings in \(b\)-metric spaces with Applications
OMA-Vol. 5 (2021), Issue 1, pp. 35 – 41 Open Access Full-Text PDF
Taieb Hamaizia
Abstract: The purpose of this paper is to prove a fixed point theorem for \(C\)-class functions in complete \(b\)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.
A new forms of extended hypergeometric functions and their properties
EASL-Vol. 4 (2021), Issue 1, pp. 30 – 41 Open Access Full-Text PDF
Ahmed Ali Al-Gonah, Waleed Khadher Mohammed
Abstract: In this paper, a new forms of extended hypergeometric functions are introduced. Some functional relations, integral representations and transformation formulas for these functions are derived.
Study of inequalities for unified integral operators of generalized convex functions
OMS-Vol. 5 (2021), Issue 1, pp. 80 – 93 Open Access Full-Text PDF
G. Farid, K. Mahreen, Yu-Ming Chu
Abstract: The aim of this paper is to study unified integral operators for generalized convex functions namely \((\alpha,h-m)\)-convex functions. We obtained upper as well as lower bounds of these integral operators in diverse forms. The results simultaneously hold for many kinds of well known fractional integral operators and for various kinds of convex functions.
Strong quasi-ordered residuated system
OMS-Vol. 5 (2021), Issue 1, pp. 73 – 79 Open Access Full-Text PDF
Daniel A. Romano
Abstract: The concept of residuated relational systems ordered under a quasi-order relation was introduced in 2018 by S. Bonzio and I. Chajda. In such algebraic systems, we have introduced and developed the concepts of implicative and comparative filters. In addition, we have shown that every comparative filter is an implicative filter at the same time and that converse it does not have to be. In this article, as a continuation of previous research, we introduce the concept of strong quasi-ordered residuated systems and we show that in such systems implicative and comparative filters coincide. In addition, we show that in such systems the concept of least upper bound for any two pair of elements can be determined.
