In this paper, we generalize some results of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), Cosentino and Vetro (Filomat 28:4, 2014), and Piri and Kumam (Fixed Point Theory Appl. 2014:210, 2014) theories by applying some weaker symmetrical conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.

Prosthetic component malposition is not infrequent, because of technical flaws, especially without a computed navigation system. We assumed that an inclined interline of a prosthetic knee with components parallel in the coronal plane provides a better load distribution and lower contact pressure towards a varus malalignment. For that we studied, using finite element analysis, load intensity and distribution for three situations: ideal alignment of prosthetic components, tibial varus malposition of 3° and 8° leading to tibio-femoral varus malalignment (i.e. an unbalanced knee) and the same tibial varus malpositions, but with the femoral component also malpositioned in the coronal plane, so that they are parallel, and with equally tightened collateral ligaments (i.e. a balanced knee). We found that maximum contact pressure and underlying bone compression forces are higher for a balanced knee with an inclined interline than in ideal alignment, but lower than in an unbalanced knee. According to our results, 2- and 4-mm additional medial plateau resection on a proper balanced knee does not significantly affect the load distribution towards ideal alignment. Balancing is a key factor for prosthetic survival in cases when a certain degree of coronal malposition cannot be avoided.

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In this paper, we introduce the notion of quadratic quasicontractive mapping and prove two generalizations of some classical fixed point theorems. Furthermore, we present some examples to support our main results.Before stating the main results, we introduce the following type of quasicontraction.Definition 1. A mapping T : X → X of a metric space X into itself is said to be a quadratic quasicontractive if there exists a ∈ 0, 1 2 such thatfor all x, y ∈ X and a strict quadratic quasicontraction if in Relation (3) we have the strict inequality for all x, y ∈ X with x = y.Lemma 1. If α, β, γ ∈ R, α, β, γ ≥ 0, a ∈ 0, 1 2 and b ∈ (0, 1) , then

The study was designed to assess the validity of a finite element analysis for predicting the behavior of cemented knee implant used in total knee arthroplasty (TKA), for different mechanical loads, and correlation with clinical outcomes of this procedure. We conducted computational simulations using finite element analysis of two situations: i) The ideal prosthetic component positioning; and ii) variable varus tibial malposition, but with a balanced knee. A total of 80 cemented TKAs performed on 70 patients were divided into two groups. Patients from one group required secondary asymmetric tibial recut for balancing the prosthetic knee and patients from the other group, did not. In regards to the results, we observed no differences upon analysis of the postoperative results of the Knee Society Score (KSS), the angle between the femur and tibia, the range of motion and frontal laxity between groups. The finite element analysis showed that in a 3˚ varus inclination of the joint interline, but with a balanced knee, the maximum contact stress, measured on the tibial plateau surface, increased by 11% compared to the value of mechanical alignment. In conclusion, analysis of the computational model using finite elements showed predictable results of cemented TKA for the different situations of mechanical loads.