Mathematica Moravica, Vol. 22, No. 1 (2018)
Strong convergence theorems for two finite families of generalized asymptotically quasi-nonexpansive mappings with applications
Mathematica Moravica, Vol. 22, No. 1 (2018), 1–14.
doi: http://dx.doi.org/10.5937/MatMor1801001S
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Abstract and keywords
Abstract. In this paper, an implicit iteration process has been proposed for two finite families of
generalized asymptotically quasi-nonexpansive mappings and establish some strong convergence theorems in the framework of convex metric spaces.
Also, some applications of our result has been given. Our results extend and generalize several results from the current existing literature.
Keywords. Generalized asymptotically quasi-nonexpansive mapping, implicit iteration process, common fixed point,
convex metric space, strong convergence.
Best proximity points of $\alpha-$$\beta-$$\psi-$proximal contractive mappings in partially ordered complete metric spaces
Mathematica Moravica, Vol. 22, No. 1 (2018), 15–29.
doi: http://dx.doi.org/10.5937/MatMor1801015B
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Abstract and keywords
Abstract. In this paper, we define $\alpha-$$\beta-$$\psi-$proximal contractive mappings in partially
ordered metric spaces and prove the existence of best proximity points of these maps in partially ordered complete metric spaces.
These results extend/generalize the results of Asgari and Badehian, J. Nonl. Sci. and Appl., 2015.
We provide illustrative examples in support of our theorems.
Keywords. Best proximity point, proximal contractive maps, admissible map, partially ordered complete metric space.
Well-posedness and asymptotic stability for the Lamé system with internal distributed delay
Mathematica Moravica, Vol. 22, No. 1 (2018), 31–41.
doi: http://dx.doi.org/10.5937/MatMor1801031T
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Abstract and keywords
Abstract. In this work, we consider the Lamé system in 3-dimension bounded
domain with distributed delay term. We prove, under some appropriate
assumptions, that this system is well-posed and stable. Furthermore,
the asymptotic stability is given by using an appropriate Lyapunov functional.
Keywords. Lamé system, delay terms, Lyapunov functions, decay rates.
Generalized $C^{\psi}_{\beta}-$ rational contraction and fixed point theorem with application to second order differential equation
Mathematica Moravica, Vol. 22, No. 1 (2018), 43–54.
doi: http://dx.doi.org/10.5937/MatMor1801043M
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Abstract and keywords
Abstract. In this article, generalized $C^{\psi}_{\beta}$- rational contraction is defined and
the existence and uniqueness of fixed points for self map in partially ordered metric spaces are discussed.
As an application, we apply our result to find existence and uniqueness of solutions of second order differential equations with boundary conditions.
Keywords. Fixed point, $C^{\psi}_{\beta}-$ rational contraction, partially ordered metric spaces, differential equations.
Relation between $b$-metric and fuzzy metric spaces
Mathematica Moravica, Vol. 22, No. 1 (2018), 55–63.
doi: http://dx.doi.org/10.5937/MatMor1801055H
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Abstract and keywords
Abstract. In this work we have considered several common fixed point results in $b$-metric
spaces for weak compatible mappings. By applications of these results we establish some fixed point theorems in $b$-fuzzy metric spaces.
Keywords. Fuzzy contractive mapping, complete fuzzy metric space, common fixed point theorem, weakly compatible maps.
Hermite-Hadamard type inequalities for $\left(m,M\right) $-$\Psi $-convex functions when $\Psi=-\ln$
Mathematica Moravica, Vol. 22, No. 1 (2018), 65–79.
doi: http://dx.doi.org/10.5937/MatMor1801065S
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Abstract and keywords
Abstract. In this paper we establish some Hermite-Hadamard type inequalities for
$ \left( m,M\right) $-$\Psi $-convex functions when $\Psi =-\ln .$
Applications for power functions and weighted arithmetic mean and geometric mean are also provided.
Keywords. Convex functions, special convexity, weighted arithmetic and geometric means, logarithmic function.
Fixed point theorems of generalised $S-\beta-\psi$ contractive type mappings
Mathematica Moravica, Vol. 22, No. 1 (2018), 81–92.
doi: http://dx.doi.org/10.5937/MatMor1801081K
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Abstract and keywords
Abstract. In this paper, we introduce the concept of generalised $S-\beta-\psi$ contractive type mappings.
For these mappings we prove some fixed point theorems in the setting of $S$-metric space.
Keywords. Generalised $S-\beta-\psi$ contractive mappings, $S$-metric space, fixed point, $\alpha$-admissible, $\beta$-admissible.
An analytical approach for systems of fractional differential equations by means of the innovative homotopy perturbation method
Mathematica Moravica, Vol. 22, No. 1 (2018), 93–105.
doi: http://dx.doi.org/10.5937/MatMor1801093D
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Abstract and keywords
Abstract. We have applied the new approach of homotopy perturbation method (NAHPM) for
partial differential system equations featuring time-fractional derivative.
The Caputo-type of fractional derivative is considered in this paper.
A combination of NAHPM and multiple fractional power series form has been used the first time to present analytical solution.
In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given.
All numerical calculations in this manuscript have been carried out with Mathematica.
Keywords. System of fractional differential equations, new homotopy perturbation method, Caputo derivative.
$(f,g)$-derivation of ordered $\Gamma$-semirings
Mathematica Moravica, Vol. 22, No. 1 (2018), 107–121.
doi: http://dx.doi.org/10.5937/MatMor1801107M
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Abstract and keywords
Abstract. In this paper, we introduce the concept of $(f,g)$-derivation, which is a generalization of
$ f-$ derivation and derivation of ordered $\Gamma$-semiring and study some properties of $(f,g)-$derivation of ordered $\Gamma$-semirings.
We prove that, if $d$ is a $(f,g)$-derivation of an ordered integral $\Gamma$-semiring $M$ then $\ker d$ is a $m-k-$ideal of $M$ and we characterize $m-k-$ideal
using $(f,g)$-derivation of ordered $\Gamma$-semiring $M.$
Keywords. Ordered $\Gamma$-semiring, derivation, $\Gamma$-semiring, integral ordered $\Gamma$-semiring, $(f,g)$-derivation.