Mathematica Moravica, Vol. 17-1 (2013)
Rhoades Type Fixed Point Theorems for a Family of Hybrid Pairs of Mappings in Metrically Convex Spaces
Mathematica Moravica, Vol. 17-1 (2013), 1–10.
doi: http://dx.doi.org/10.5937/MatMor1301001K
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Abstract and keywords
Abstract. The present paper establishes some coincidence and fixed point theorems
for a sequence of hybrid type nonself mappings defined on a closed subset of a metrically convex metric spaces,
which generalize some earlier results due to Rhoades [18], Ahmed and Rhoades [1] and many others. Some related results are also derived.
Keywords. Metrically convex metric space, Quasi-coincidentally commuting mappings, Compatible mappings,
Coincidentally idempotent.
Fixed Point Theorems in Probabilistic Metric Spaces Using Property (E.A)
Mathematica Moravica, Vol. 17-1 (2013), 11–24.
doi: http://dx.doi.org/10.5937/MatMor1301011P
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Abstract and keywords
Abstract. In this paper, we prove a common fixed point theorem for even number of
self mappings in Menger space by using an implicit relation with property (E.A). We also extend our main result to four
finite families of mappings employing the notion of pairwise commuting due to Imdad et al. [Coincidence and common fixed point
theorems for nonlinear contractions in Menger PM spaces, Chaos, Solitons & Fractals 42(5) (2009), 3121-3129].
Our results generalize and extend several well known comparable results existing in literature.
Keywords. $t$-norm, probabilistic metric space, property (E.A), weakly compatible mappings,
non-compatible mappings, implicit relation.
Some Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces
Mathematica Moravica, Vol. 17-1 (2013), 25–37.
doi: http://dx.doi.org/10.5937/MatMor1301025S
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Abstract and keywords
Abstract. In this paper, we prove some fixed point theorems in complete
G-metric spaces for self mappings satisfying different contractive conditions depended an another function.
We also discuss that these mappings are G-continuous on such a fixed point.
Keywords. G-metric spaces, fixed point, G-continuous, Contractive mappings, Depended function.
Growth and Oscillation of Polynomial of Linearly Independent Meromorphic Solutions of
Second Order Linear Differential Equations in the Unit Disc
Mathematica Moravica, Vol. 17-1 (2013), 39–50.
doi: http://dx.doi.org/10.5937/MatMor1301039B
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Abstract and keywords
Abstract. In this paper, we deal with the growth and oscillation of
$w = d_{1}f_{1} + d_{2}f_{2}$, where $d_{1}$, $d_{2}$ are meromorphic functions of finite iterated $p$-order
that are not all vanishing identically and $f_{1}$, $f_{2}$ are two linearly independent meromorphic solutions
in the unit disc $\Delta = \{z \in C: |z| < 1\}$ satisfying $\delta (\infty,f_{j}) > 0$, $(j = 1, 2)$,
of the linear differential equation
\[f' + A(z)f = 0,\]
where $A(z)$ is admissible meromorphic function of finite iterated $p$-order in $\Delta$.
Keywords. Linear differential equations, Polynomial of solutions, Meromorphic solutions,
Iterated order, Iterated exponent of convergence of the sequence of distinct zeros, Unit disc.
On the Existence and Uniqueness of Solutions of Boundary Value Problems for Second Order Functional Differential Equations
Mathematica Moravica, Vol. 17-1 (2013), 51–57.
doi: http://dx.doi.org/10.5937/MatMor1301051A
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Abstract and keywords
Abstract. In this paper we study existence and uniqueness of solutions of
boundary value problems for second order nonlinear delay differential equations. We transform the boundary value problem to
an equivalent integral equation and then we use the Banach fixed point theorem and the notion of the Fréchet derivative.
Keywords. Functional differential equation, integral equation, contractive operator.
Certain Topological Qualities of Convex Sets in Euclidean Space
Mathematica Moravica, Vol. 17-1 (2013), 59–62.
doi: http://dx.doi.org/10.5937/MatMor1301059E
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Abstract and keywords
Abstract. In this paper, we give four theorems relevant to certain topological
qualities of the convex sets in Euclidean space. All results remain to hold in any locally convex space.
They show that pair of convex sets under definite conditions satisfies some supplement qualities.
Keywords. Convex subsets of Euclidean space.
On Separation Axioms in Fuzzifying Generalized Topology
Mathematica Moravica, Vol. 17-1 (2013), 63–74.
doi: http://dx.doi.org/10.5937/MatMor1301063G
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Abstract and keywords
Abstract. In this paper we introduce and study the concept of fuzzifying separation
axioms in fuzzifying generalized topological spaces.
Keywords. Lukasiewicz logic, generalized, fuzzifying Generalized topology, fuzzifying $\mu$-open sets.
Asymptotic Properties of Rapidly Varying Functions
Mathematica Moravica, Vol. 17-1 (2013), 75–78.
doi: http://dx.doi.org/10.5937/MatMor1301075V
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Abstract and keywords
Abstract. In this paper we study asymptotic properties of rapidly varying functions.
The important properties of this class that are related to arithmetic mean will be proved.
The asymptotic properties of series $\sum_{n=1}^{\infty}f(n)$ when $f$ rapidly varying functions will be proved, also.
Keywords. Rapidly varying functions, asymptotic properties.
Some Common Fixed Point Theorems for Converse Commuting Mappings Via Implicit Relation
Mathematica Moravica, Vol. 17-1 (2013), 79–87.
doi: http://dx.doi.org/10.5937/MatMor1301079L
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Abstract and keywords
Abstract. In this paper, we utilize a class of implicit function studied by Imdad et al.
[Some common fixed point theorems in Menger PM spaces, Fixed Point Theory Appl. Vol. 2010, Article ID 819269, 14 pages] and
prove a common fixed point theorem for converse commuting mappings in Menger space. We give an example which demonstrate
the validity of the hypotheses and degree of generality of our main result.
Keywords. $t$-norm, Menger space, converse commuting mappings, implicit relation, fixed point.
Some Properties of Second Order Differential Equations
Mathematica Moravica, Vol. 17-1 (2013), 89–94.
doi: http://dx.doi.org/10.5937/MatMor1301089A
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Abstract and keywords
Abstract. In this paper we established the Hyers-Ulam-Rassias stability of
a linear differential equation of second order with initial condition.
We also proved the Hyers-Ulam-Rassias stability of a nonlinear differential equation of second order with initial condition.
Keywords. Differential equations, Hyers-Ulam-Rassias stability, Linear, Nonlinear, Second order.