Fixed Point Theorems on Some New Types of Cyclic Contractions and Their Generalization

There are different types of contraction in the existing literature for the generalization of Banach’s contraction principle. Our aim in this paper is to generalize cyclic contraction so that it can explain all types of cyclic contraction as a particular case. Besides all contractions in the existing literature we introduce some new types of cyclic contraction before defining the generalized cyclic contraction.

Symmetric Spaces Approach to Various Cyclic Contractions and Application to Probabilistic Spaces

This paper aims to prove fixed point results for cyclic compatible contraction and Hardy–Rogers cyclic contraction in symmetric spaces. Our results generalize the results of Kumari and Panthi (2016) proved for cyclic compatible contraction and modified Hardy–Rogers cyclic contraction in the generating space of a b-quasi metric family and b-dislocated metric family. After that, as an application, we prove a fixed point result in symmetric pre-probabilistic metric spaces (PPM-spaces).

The energy of muscle contraction. IV. Greater mass of larger muscles decreases contraction efficiency

While skeletal muscle mass has been shown to decrease mass-specific mechanical work per cycle, it is not yet known how muscle mass alters contraction efficiency. In this study, we examined the effect of muscle mass on mass-specific metabolic cost and efficiency during cyclic contractions in simulated muscles of different sizes. We additionally explored how tendon and its stiffness alters the effects of muscle mass on mass-specific work, mass-specific metabolic cost and efficiency across different muscle sizes. To examine contraction efficiency, we estimated the metabolic cost of the cycles using established cost models. We found that for motor contractions in which the muscle was primarily active during shortening, greater muscle mass resulted in lower contraction efficiency, primarily due to lower mass-specific mechanical work per cycle. The addition of a tendon in series with the mass-enhanced muscle model improved the mass-specific work and efficiency per cycle with greater mass for motor contractions, particularly with a shorter excitation duty cycle, despite higher predicted metabolic cost. The results of this study indicate that muscle mass is an important determinant of whole muscle contraction efficiency.

Characterization of particles and their relation with residual aluminum in water treated with pulsating floc blanket clarifiers and conventional clariflocculators using PACl

A pulsating floc blanket clarifier (PFBC) employing cyclic contractions and rarefactions to a bed of densely concentrated suspension of flocculated particles in fluidized state, was compared with conventional clariflocculator (CC) at pilot scale (8,000 L/day) in continuous mode of operation. For influent turbidity varied from 2 to 20 NTU, coagulation-flocculation behavior exhibited under the two fundamentally different treatment processes with PACl influenced inter-related performance parameters. The residual turbidity was found lower by 74%, flocs and fine colloids in suspension larger by 73 and 75% respectively, and the total and dissolved residual aluminum lower by 50 and 49% respectively on average for PFBC compared to CC. Particulate form comprised major fraction (≈72%) of total residual aluminum for both. PFBC abetted formation of a more consolidated floc structure which rendered the shape, size and morphology such that the settling velocity was 50% to 410% higher than that of the CC flocs. Reaction-limited aggregation (RLA) process and inter-particle bridging were dominant and the resulting floc structure and its formation mechanism have been presented.

Existence of Coupled Best Proximity Points of p-Cyclic Contractions

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

Coincidence best proximity point theorems for proximal Berinde g-cyclic contractions in metric spaces

In this paper, we introduce the notions of proximal Berinde g-cyclic contractions of two non-self-mappings and proximal Berinde g-contractions, called proximal Berinde g-cyclic contraction of the first and second kind. Coincidence best proximity point theorems for these types of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our main results extend and generalize many existing results in the literature.

Generalized cyclic contractions and coincidence points involving a control function on partial metric spaces

PurposeIn this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.Design/methodology/approachTheoretical method.FindingsWe establish some coincidence points and common fixed point results in partial metric spaces.Originality/valueResults of this study are new and interesting.