Lacunary ℐ -Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ -invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ -invariant convergence W ℐ σ θ η , ν (Wijsman sense), lacunary ℐ ∗ -invariant convergence W ℐ σ θ ∗ η , ν (Wijsman sense), and q -strongly lacunary invariant convergence W N σ θ η , ν q (Wijsman sense) of sequences of sets in IFMS. Also, we give the relationships among Wijsman lacunary invariant convergence, W N σ θ η , ν q , W ℐ σ θ η , ν , and W ℐ σ θ ∗ η , ν in IFMS. Furthermore, we define the concepts of W ℐ σ θ η , ν -Cauchy sequence and W ℐ σ θ ∗ η , ν -Cauchy sequence of sets in IFMS. Furthermore, we obtain some features of the new type of convergences in IFMS.

Statistical convergence in probabilistic generalized metric spaces w.r.t. strong topology

In this paper, the concept of probabilistic g-metric space with degree l, which is a generalization of probabilistic G-metric space, is introduced. Then, by endowing strong topology, the definition of l-dimensional asymptotic density of a subset A of $\mathbb{N}^{l}$ N l is used to introduce a statistically convergent and Cauchy sequence and to study some basic facts.

New Contributions in Generalization S -Metric Spaces to S ∗ p -Partial Metric Spaces with Some Results in Common Fixed Point Theorems

In this paper, we introduce the notion of S ∗ p -partial metric spaces which is a generalization of S-metric spaces and partial-metric spaces. Also, we give some of the topological properties that are important in knowing the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorems in this spaces.

Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application

This manuscript investigates fixed point of single-valued Hardy-Roger’s type F -contraction globally as well as locally in a convex b -metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F -contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b -metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations.

Completeness of P-Summable as Hilbert Space with Its Dual Space

Hilbert space is a complete inner product space, meaning that each Cauchy sequence converges to a point in that space. One of the vector spaces that will be examined as the inner product space is p-summable space. The inner product space is a subset of vector spaces that have special properties that must be fulfilled. One way to prove vector space is the inner product space is to use parallelogram equality theorems. After it is known that the vector space is the inner product space, the completeness of the space will be proven using the dual space. The space used is the p-summable space, data that can be changed in a sequence form will be usable in this study. The results of this study will be useful as another application in determining a Hilbert space by using a method that is different from the definition. The analysis used will show comparison of the speed of completion accuracy will be a benchmark in this study, so that will be a new reference in determining a space is Hilbert space.

A new type of difference I-convergent sequence in IFnNS

In this paper, we introduce the notion of a generalized difference I-convergent (i.e.?m-I-convergent) and difference I-Cauchy (i.e.?m-I-Cauchy) sequence in intuitionistic fuzzy n-normed spaces. Further, we prove some results related to this notion. Also, we study the concepts of a generalized difference I+-convergent (i.e.?m-I+-convergent) sequence in intuitionistic fuzzy n-normed spaces and show the relation between them.

Approximate controllability of fractional neutral evolution systems of hyperbolic type

<p style='text-indent:20px;'>In this paper, we deal with fractional neutral evolution systems of hyperbolic type in Banach spaces. We establish the existence and uniqueness of the mild solution and prove the approximate controllability of the systems under different conditions. These results are mainly based on fixed point theorems as well as constructing a Cauchy sequence and a control function. In the end, we give an example to illustrate the validity of the main results.</p>

Almost convergence of complex uncertain double sequences

Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable. Almost convergence with respect to almost surely, mean, measure, distribution and uniformly almost surely are presented and interrelationships among them are studied and depicted in the form of a diagram. We also define almost Cauchy sequence in the same format and establish some results. Conventionally we have, every convergent sequence is a Cauchy sequence and the converse case is not true in general. But taking complex uncertain variable in a double sequence, we find that a complex uncertain double sequence is a almost Cauchy sequence if and only if it is almost convergent. Some suitable examples and counter examples are properly placed to make the paper self sufficient.

λ-quasi Cauchy sequence of fuzzy numbers

In this paper we introduce the λ -quasi Cauchy sequence of fuzzy numbers. We obtain the relation between strongly λ-quasi Cauchy convergence and statistically λ -quasi Cauchy convergence for fuzzy numbers.

Some Existence Results for a System of Nonlinear Fractional Differential Equations

In this paper, we show that a sequence satisfying a Suzuki-type JS-rational contraction or a generalized Suzuki-type Ćirić JS-contraction, under some conditions, is a Cauchy sequence. This paper presents some common fixed point theorems and an application to resolve a system of nonlinear fractional differential equations. Some examples and consequences are also given.