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In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example.

In this paper we consider a best proximity point problem whose purpose is to determine the minimum distance between two sets. It is a global optimization problem by its very nature which is solved by converting it into a problem of finding an optimal approximate solution of a fixed point inclusion for a coupled setvalued mapping. Two solutions are obtained simultaneously through an iteration. We introduce certain definitions which are used in our theorems. We investigate the data dependence property of the proximity point sets and establish a weak stability result for the proximity point sets. There are some illustrative examples. The broad area of the present study is setvalued optimization.

In this paper, we discuss a protocol for preparing a non-maximally entangled W-state at a distant location where there are two parties intending such creation each of whom possesses only partial information about the state. These two parties along with a third party Controller, participate in a single protocol in order to create the intended state in the hands of a fourth party. The role of the controller is to fabricate an 8-qubit entangled state and distribute the respective qubits involved in the entangled state to the relevant parties and thereby creating a noisy quantum channel. The protocol is first ideally discussed in the noise-free case which is then a perfect joint remote state preparation protocol with fidelity 1. Then, we discuss the performance of the protocol in the presence of noise in which the fidelity is diminished. We consider three different types of noises and analyze the variation of fidelity of the process. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a proposal for the transfer of states belonging to the W-type states by executing a controlled teleportation protocol. A 7-qubit quantum entangled resource shared between the sender, receiver and controller is utilized in this protocol. The scheme proposed here is a perfect communication scheme where the task of quantum state transfer is performed with certainty. Further, a protocol for the generation of the quantum resource used here is designed and run on IBM platform. Additionally, we consider the effect of four types of noises, namely, amplitude-damping noise, bit-flip noise, phase-flip noise and phase-damping noise on our protocol. The efficiency of the protocol is compared with other similar protocols which shows that the present one is better performing. [ABSTRACT FROM AUTHOR]

In the present work we solve the problem of finding the fuzzy distance between two subsets of a fuzzy metric space for which we use a non-self fuzzy contraction mapping from one set to the other. It is a fuzzy extension of the proximity point problem which is by its nature a problem of global optimization. The contraction is defined here by two control functions. We define a geometric property of the fuzzy metric space. The main result is illustrated with an example. Our result extends a fuzzy version of the Banach contraction mapping principle.

In this paper, we use an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines several ideas prevalent in fixed point theory studies. There are several corollaries and illustrative examples. The Hausdorff-Pompeiu metric between sets is used. The work is in the context of metric spaces and is a part of set-valued analysis with the singlevalued consequences. [ABSTRACT FROM AUTHOR]