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The purpose of this paper is to study the dynamical representation of frames in tensor product of two Hilbert spaces H 1 ⊗ H 2 . We have considered frames in H 1 ⊗ H 2 and established that they have dynamical representations and can be generated by some frame elements. In addition, we determined their canonical dual frames and showed that the canonical dual frames have also iterative structures. We have investigated the Dynamical frames (frames generated by iterative actions of operators) and scalable frames in H 1 ⊗ H 2 and gave the characterization of operators to ensure that the dynamical structure and scalability of a frame are preserved. Later on, we have extended the concept of Dynamical frames to frames generated by a sequence of operators in H 1 ⊗ H 2 , and established some results regarding their canonical dual frames and their representations. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness solutions of trifunction equilibrium problems using the generalized relaxed α -monotonicity in Banach spaces. By using the generalized f-projection operator, a hybrid iteration scheme is presented to find a common element of the solutions of a system of trifunction equilibrium problems and the set of fixed points of an infinite family of quasi- ϕ -nonexpansive mappings. Moreover, the strong convergence of our new proposed iterative method under generalized relaxed α -monotonicity is considered. [ABSTRACT FROM AUTHOR]