# Mathematica Moravica, Vol. 20:2 (2016)

Uniqueness of the power of meromorphic functions with its differential polynomial sharing a set
Mathematica Moravica, Vol. 20-2 (2016), 1-14

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Abstract. This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are posed for future research.
Keywords. Meromorphic function, differential polynomial, set sharing, uniqueness.

Coefficient problem for certain subclasses of bi-univalent functions defined by convolution
Mathematica Moravica, Vol. 20-2 (2016), 15-21

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Abstract. In this paper, we consider a general subclass $H_{\Sigma}^{\lambda}(h,\beta)$ of bi-univalent functions. Bounds on the first two coefficients $|a_{2}|$ and $|a_{3}|$ for functions in $H_{\Sigma}^{\lambda}(h,\beta)$ are given. The main results generalize and improve a recent one obtained by Srivastava [18].
Keywords. Analytic and univalent functions, bi-univalent functions, convolution.

Some congruences related to harmonic numbers and the terms of the second order sequences
Mathematica Moravica, Vol. 20-2 (2016), 23-37
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Abstract. In this paper, with helps of some combinatorial identities, we investigate various basic congruences involving harmonic numbers and terms of the second order sequences $\{U_{kn}\}$ and $\{V_{kn}\}$.
Keywords. Congruences, harmonic numbers, second order sequences.

Optimal Harvesting Policy for the Beverton–Holt quantum difference model
Mathematica Moravica, Vol. 20-2 (2016), 39-57

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Abstract. In this paper, we introduce exploitation to the Beverton-Holt equation in the quantum calculus time setting. We first give a brief introduction to quantum calculus and to the Beverton-Holt $q$-difference equation before formulating the harvested Beverton-Holt $q$-difference equation. Under the assumption of a periodic carrying capacity and periodic inherent growth rate, we derive its unique periodic solution, which globally attracts all solutions. We further derive the optimal harvest effort for the Beverton-Holt $q$-difference equation under the catch-per-effort hypothesis. Examples are provided and discussed in the last section.
Keywords. Beverton-Holt, quantum calculus, periodic solution, stability, optimal harvest yield.

A common coupled fixed point theorem in intuitionistic Menger metric space
Mathematica Moravica, Vol. 20-2 (2016), 59-85

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Abstract. We establish a common fixed point theorem for mappings under $\phi$-contractive conditions on intuitionistic Menger metric spaces. As an application of our result we study the existence and uniquenes of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.
Keywords. Intuitionistic Menger metric space, common coupled fixed points, $\phi$-contractive condition, weak compatibility.

$\mathcal{I} — Fréchet-Urysohn Spaces Mathematica Moravica, Vol. 20-2 (2016), 87-97 Download PDF file: (471kB) | Abstract and keywords Abstract. In this paper, we introduce the concept ss-sequentially quotient mapping. Using this concept, we characterize s-Fréchet-Urysohn spaces and s-sequential spaces. Finally, we develop the properties of$\mathcal{I}$-Fréchet-Urysohn spaces which is the generalized form of s-Fréchet-Urysohn spaces. Also, we give an example that product of two$\mathcal{I}$-Fréchet-Urysohn spaces need not be an$\mathcal{I}$-Fréchet-Urysohn space for any$\mathcal{I}$. Keywords. Sequentially quotient, sequential space, Fréchet-Urysohn space, s-convergence,$\mathcal{I}$-convergence. Multi-criteria decision making method of minimal suitable values Mathematica Moravica, Vol. 20-2 (2016), 99-107 Download PDF file: (418kB) | Abstract and keywords Abstract. This paper presents a conceptual and mathematical model of a multi-criteria decision making process in which the information about decision maker's preferences is expressed in the form of minimal suitable values. Keywords. Multicriteria analysis, alternative, criterion, weight. Some New Fixed Point Theorems in Metric Spaces Mathematica Moravica, Vol. 20-2 (2016), 109-121 Download PDF file: (429kB) | Abstract and keywords Abstract. In this paper, the main results of [13] are generalized. Also, examples are given to illustrate the obtained results. Keywords. Fixed point, metric, partial metric. New Symmetric Identities of Carlitz’s Generalized Twisted$q$-Bernoulli Polynomials under$S_{3}$Mathematica Moravica, Vol. 20-2 (2016), 123-129 Download PDF file: (441kB) | Abstract and keywords Abstract. In this paper, the authors consider the Carlitz's generalized twisted$q$-Bernoulli polynomials attached to$\chi$and investigate some novel symmetric identities for these polynomials arising from the$p$-adic$q$-integral on$\mathbb{Z}_{p}$under$S_{3}$. Keywords. Symmetric identities, Carlitz's generalized twisted$q$-Bernoulli polynomials,$p$-adic$q$-integral on$\mathbb{Z}_{p}$, invariant under$S_{3}\$.

Hybrid Mixed Type Iteration Scheme for Asymptotically Nonexpansive Mappings and Total Asymptotically Nonexpansive Non-self Mappings
Mathematica Moravica, Vol. 20-2 (2016), 131-141

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Abstract. In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some strong convergence theorems for mentioned scheme and mappings in real Banach spaces. Our results extend and generalize several results from the current existing literature.
Keywords. Asymptotically nonexpansive mapping, total asymptotically nonexpansive non-self mapping, hybrid mixed type iteration scheme, common fixed point, Banach space, strong convergence.

Existence and Exponential Stability of Solutions for Transmission System with Varying Delay in R
Mathematica Moravica, Vol. 20-2 (2016), 143-161

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Abstract. In the present paper we are going to consider in a one dimension bounded domain a transmission system with a varying delay. Under suitable assumptions on the weights of the damping and the delay terms, we prove the well-possedness and the uniqueness of solution using the semigroup theory. Also we show the exponential stability by introducing an appropriate Lyaponov functional.
Keywords. Wave equation, transmission problem, varying delay term, exponential stability.

Note on “Common Fixed Point Theorem for Weakly Compatible Multi-Valued Mappings Satisfying Strongly Tangential Property”
Mathematica Moravica, Vol. 20-2 (2016), 163-165

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Abstract. In our paper [1], the existence and uniqueness of a common fixed point for multi valued mappings was given, hence in this note we point out to no uniqueness of common fixed point in Theorem 3.1, Corollary 3.1 and Corollary 3.2. We provide an example to demonstrate our purpose.
Keywords. Common fixed point, strongly tangential, weakly compatible, multi-valued maps.